ETD Collection

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    Comparitive analysis of bornology in the categories of frolicher spaces and topological spaces
    (2024) Mahudu, Ben Moditi
    This thesis seeks to introduce the concept of bornology to the theory of Fr¨olicher spaces. Bornologies are induced from the Fr¨olicher structure, Fr¨olicher topology and the canonical topology on the underlying set of Fr¨olicher space. In each case the bornologies are compared in a general Fr¨olicher space, subspace, product, coproduct and quotient. The Fr¨olicher topology refers to the topology induced from structure functions of the Fr¨olicher space. The bornology induced from the Fr¨olicher structure is induced from the structure functions of Fr¨olicher space. An initial bornology is canonically induced on the underlying set of Fr¨olicher subspace and product, and a final bornology is induced canonically on the underlying set of Fr¨olicher coproduct and quotient. For Fr¨olicher subspace and product the initial bornology is finer than the bornology induced from structure functions. Dually, the final bornology is coarser than the bornology induced from structure functions for Fr¨olicher coproduct and quotient. Relatively-compact and compact bornologies are induced from the Fr¨olicher topology and the canonical topology on the underlying set of Fr¨olicher space. For each of Fr¨olicher subspace, product, coproduct and quotient, that is, the objects in the category of Fr¨olicher spaces under the study of this thesis, there are two topologies - the canonical topology induced from the underlying set and the Fr¨olicher topology. Subsequently there are two relatively-compact and compact bornologies, induced from these topologies, for each of the mentioned objects. The bornological comparison between the relatively-compact bornologies and the bornological comparison between the compact bornologies, for each object, is determined by the comparison of these topologies, that is, the comparison between the Fr¨olicher topology and the canonical topology on the underlying set.
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    Augmentative topology agents for open-ended learning
    (2024) Nasir, Muhammad Umair
    We tackle the problem of open-ended learning by improving a method that simultaneously evolves agents and increasingly challenging environments. Unlike previous open-ended approaches that optimize agents using a fixed neural network topology, we hypothesize that the open-endedness and generalization can be improved by allowing agents’ controllers to become more complex as they encounter more difficult environments. Our method, Augmentative Topology EPOET (ATEP), extends the Enhanced Paired Open-ended Trailblazer (EPOET) algorithm by allowing agents to evolve their own neural network structures over time, adding complexity and capacity as necessary. Empirical results demonstrate that ATEP results in open-ended and general agents capable of solving more environments than a fixed-topology baseline. We also investigate mechanisms for transferring agents between environments and find that a species-based approach further improves the open-endedness and generalization of agents.
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    Topology-inspired probabilistic path replanning in dynamic environments
    (2018) Fisher, Richard
    Path replanning in high dimensional dynamic environments is critical to the success of interactive and reactive robotic agents. State of the art replanning algorithms typically extend sampling-based methods such as rapidly-exploring random trees (RRT) or probabilistic roadmaps (PRM). However, the speed of replanning in complex configuration spaces is relatively slow, which limits the effectiveness of robotic agents in highly dynamic environments. This thesis proposes DRM-connect, a novel generalisation of the PRM and RRT-connect algorithms, which carries out replanning in dynamic environments by executing graph searches over an underlying graph G, using lazy collision checking. If a path through the graph is not found, DRM-connect will repair the graph using a novel extension to RRT-connect, which we call PRM-connect. Additionally, we investigate using an approximate Reeb graph as the underlying graph G, which attempts to capture the underlying topology of the task manifold from prior experience. DRM-connect is tested with both a Reeb graph and na¨ıve graph in a 2-D domain and compared to RRT, while DRMconnect with a Reeb graph is tested in three 7-D domains, and compared to RRT-connect. Through simulation we show that the combination of DRM-connect and a Reeb graph typically outperforms both RRT/RRT-connect and DRM-connect with a na¨ıve graph in terms of replanning times, with minimal impact on the length of the solution path.